Sunflower is a major agricultural oilseed crop, and the Republic of Kazakhstan has been steadily strengthening its position as a producer of oilseeds. In this study, an oil pressing machine with two processes, including grinding sunflower seeds and pressing the obtained cake to separate the oil, is constructed. The experiment investigated the impact of different grinding degrees (hole diameters of plates of 5 mm, 4 mm, 3 mm, and 2 mm) and screw rotation speeds (ranging from 30 rpm to 250 rpm) on oil pressing efficiency. The study used sunflower seeds with an oil content of 45–47% and moisture of 7–9%. The results showed that increasing the grinding degree and screw rotation speed led to higher oil yield. The optimal condition was a grinding degree of 4 mm and a screw rotation speed of 60 rpm, resulting in the highest oil yield of 15.6 g/s. Additionally, the residual oil content of the seed cake decreased significantly as pressure increased during pressing, particularly with 4 mm grinding. Power consumption increased with higher screw rotation speeds and finer grinding degrees, indicating the influence of grinding components on energy demand. The cake density increased with higher screw rotation speeds and finer grinding degrees, highlighting the impact of grinding mechanisms on cake compactness. Moreover, the temperature of the cake rose with increased screw rotation speed and the presence of grinding sieves. These findings provide valuable insights into optimizing the sunflower oil pressing process, highlighting the importance of selecting appropriate grinding degrees and screw rotation speeds to maximize oil yield and pressing efficiency.